IIUC, should work great. I run a sub from the "Output 1" (Outputs 1 and 2 are on/off switchable, and are volume-controlled with the C220 volume control).
You would have to hook up (say) the 275 to Output 1 and the SS amp to Output 2, and select which (or both) to listen to. Don't use the 'Tape' output which is fixed! Unless it goes to a powered sub with its own controls (which will not track the C220 volume setting).
The only thing I can think of that may be an issue is amp & speaker sensitivity. Since the 275 has controls for that (and maybe the SS amp does too?), shouldn't be a problem.
Say your SS amp is fixed (no adjustment). Hook up the SS amp (say) to Output 2, start with the C220 at low volume, and adjust the volume to taste. Keep or note the C220 volume setting. Switch Output 2 off, Output 1 on (with the 275's controls turned 'down') and adjust the 275's controls to the desired volume. Voila!
If the 275 'runs out' of adjustment or the controls are barely engaged, there might be too great a mismatch in sensitivity between the amp/speaker combinations. Then you could use the C220 volume to compensate (remember to adjust before switching amps!), or insert an attenuator inline with one of them ... but this seems to be too complicated ...?
Sorry if this was 'too detailed' for you, but wanted to try to walk thru the steps just in case.
I think the C220 was designed with this in mind, so no worries about hurting anything.
HTH, - Rick.